Question

One-fourth length of a spring of force constant $k$ is cut away. The force constant of the remaining spring will be

• A. $\frac{3}{4}k$
• B. $\frac{4}{3}k$
• C. k
• D. 4k

Answer 1

Answer: (B)

$\frac{4}{3}k$

Answer 2

Spring constant $k \propto \frac{1}{l}$ Therefore, $\frac{k_{2}}{k_{1}}=\frac{l_{1}}{l_{2}}$ Given, $l_{1}=l, l_{2}=3 / 4 l, k_{1}=k$ $\therefore$ $\frac{k_{2}}{k}=\frac{l}{3 / 4 l}$ or $k_{2}=\frac{4}{3} k$